My primary opposition to the Warlord is the flavor attached to it, not the mechanics.
What I don't like is the notion that a character is the "leader" by dint of having chosen a certain class. "Oh, that's just a word, you can re-fluff it however you want" proponents say. Except it's hard to believe they really think that, given how they describe the class:
- "Warlord" itself is aggrandizing beyond any other class name, and the alternatives offered, which nearly all suggest some kind of rank, are just as bad. If the Warlord is the "Officer" or "Captain" what does that make the Fighter? The Private? Yeah, I wanna play the low guy on the totem pole...
- The "officer" term in particular is often used as the real life archetype for the class. Q.E.F.D. (Logically, the problem I have with that concept is that adventuring parties are not military units.)
- When debating the warlord, and in particular the "realism" of martial healing (note: I have no opposition to martial healing itself) many, many posters use the example of the officer yelling at the raw recruit and getting him back in the battle. Again...yeah, great: I really want to play the guy who needs your character yelling at me to make me fight. Not.
- In general, the fluff of Warlord abilities gets described as telling the other characters what to do. "Order retreat", "Give command", "Bolster confidence", etc.
- When debating fictional/historical examples: the proponents cite all the coolest heroes as examples of warlords, which by process of elimination leaves only the sidekicks as other classes. Odysseus? Warlord. Aragron? Warlord. Lancelot? Warlord. Hannibal Smith? Warlord. (Not that they're right, but the fact that proponents think those characters represent the Warlord shows what they are thinking.)
I have to be honest, despite proponents' repeated claims that they just want more tactical play, it's hard not to suspect that what they really want is to just roleplay the Boss.
My only somewhat tongue-in-cheek response has been to suggest the "Caddy" class. Which, if all they want is the tactical options, and think that fluff really doesn't matter, should be fine for the Warlord fans.
Caddy Abilities:
"May I suggest the seven iron, sir?" You give another player a helpful suggestion, which gives them Advantage on their next Attack.
"Mind the sand bar" You point something out to an ally, giving them Advantage on Perception rolls for 1 round.
"Gin & tonic?" Restore 1d8 HP to an ally.
Etc.
Except, strangely, no Warlord fans have ever gotten excited about this idea.
So, my vote is No.